The present invention relates to a method and apparatus for discharge machining in which a workpiece is machined obliquely or in a tapered shape by applying electric current to the workpiece and the machining electrode, and by moving the electrode relative to the workpiece in a main machining direction and also in a direction substantially perpendicular to the main machining direction.
In a conventional discharge machining method, a workpiece is machined to transfer the shape of the machining electrode into the workpiece while the electrode is only moved relative to the workpiece in a primary or main machining direction. Discharge machining utilizing the relative movement of the electrode relative to the workpiece in a plane perpendicular to the main machining direction is also known, as disclosed in Japanese Published Patent Application No. 3594/1966.
An example of the conventional discharge machining method will be described with reference to FIG. 1, in which a workpiece 12 is machined with an electrode 10 to a depth Zm in a tapered shape 14 having a radius R.sub.0 (the length of movements of the electrode in a direction perpendicular to the main machining direction). At the time of starting the machining operation the length of displacement of the electrode is controlled in a direction perpendicular to the main machining direction in response to the depth of machining of the workpiece in such a manner to be larger at the time of starting the machining and smaller as the machining operation advances. More specifically, the electrode 10 is moved relative to the workpiece in a primary machining or Z-axis direction, and is also moved generally circularly in a plane substantially perpendicular to the Z-axis direction, or in X-axis and Y-axis directions. Thus, the electrode 10 is moved relative to the workpiece in a combination of these three axial directions, and the workpiece is thereby machined in the aforementioned tapered shape 14.
FIG. 2 shows an example of the discharge machining apparatus for practicing the above-described discharge machining method and machining the tapered shape 14 in the workpiece. In FIG. 2 an electrode 10 is mounted through a supporting base 16 at a hydraulic servo mechanism to move relative to a workpiece 12. The hydraulic servo mechanism includes a hydraulic servo valve 18 and a hydraulic cylinder 20. The electrode supporting base 16 is mounted at the end of the piston rod 22 of the hydraulic cylinder 20. The supporting base 16 includes a base 16X which moves in an X-axis direction and a base 16Y which moves in a Y-axis direction. Feeding nuts (not shown) are provided at the side surfaces of the respective bases 16X and 16Y. Feeding screws 24 and 26 are engaged with the nuts, respectively, and are rotationally driven by servo motors 28 and 30, respectively.
In operation, the electrode 10 is confronted with the workpiece 12 to be matched in a machining or insulating solution with a machining gap g formed therebetween. An electric discharge or an electrolysis occurs in the gap g between the electrode 10 and the workpiece 12. A pulse current supplied from a pulse current supply source 32 flows therebetween and the electrode 10 machines the workpiece 12 through the discharge or the electrolysis action.
At this time a voltage Vd corresponding to the machining gap g and a reference voltage Vs are applied to a voltage differential circuit 34, which produces an output Vd-Vs. This output is sequentially applied to an amplifier 36 and to the hydraulic servo valve 18, thereby controlling the servo valve in accordance with the amplified differential voltage. Thus, the hydraulic cylinder 20 is controlled by the servo valve 18, and in turn controls the electrode 10 mounted through the base 16 via the piston rod 22 until the voltage Vd coincides with the reference voltage Vs, and accordingly the electrode 10 is moved relative to the workpiece 12 in a main machining or Z-axis direction.
After the workpiece 12 is machined coarsely to the depth set slightly before the final desired depth by the electrode 10, and the coarse machining step is thus finished, the pulse current supply source 32 is switched to produce an output having smaller energy pulses. Further, a Z-axis digital pulse scale 38 for detecting the length of movement of the electrode 10 is the Z-axis direction is provided adjacent to the electrode 10 and produces an output signal to an electrode movement control device 40, which in turn produces output signals to both the servo motors 28 and 30. The servo motors move the electrode supporting base 16X in the X-axis direction and the electrode supporting base 16Y in the Y-axis direction, thereby imparting a circular motion of radius R to the electrode 10. In this manner the workpiece 12 is machined in a tapered shape 14 to a depth Z, with the radius R of the circle larger at the top and smaller at the bottom.
FIG. 3 shows an example of the electrode movement control device 40 in block diagram form, including a two-phase oscillator 42 for producing sine waves e.sub.x and e.sub.y differing in phase by 90.degree., a control circuit 44 for producing voltage outputs E.sub.x and E.sub.y corresponding to the desired eccentric radii under the control of the sine waves e.sub.x and e.sub.y on the basis of the voltage Vd corresponding to the machining gap, addition points 50 and 52 for adding the detected outputs R.sub.x and R.sub.y from linear potentiometers 46 and 48, respectively, corresponding the lengths of the X-axis and Y-axis movements of the electrode supporting base 16, and the output voltages E.sub.x and E.sub.y from the control circuit 44, and amplifiers 54 and 56 for amplifying the outputs from the addition points 50 and 52 and applying them to the servo motors 28 and 30, respectively. With this configuration of the control circuit 40, the servo motors 28 and 30 will operate until the output voltages from the addition points 50 and 52 become zero and accordingly control the movements of the electrode supporting bases 16X and 16Y so as to become equal to the outputs E.sub.x and E.sub.y from the control circuit 44.
FIG. 4 illustrates the two-phase oscillator 42 in the control circuit 40, including an integrating circuit 58 having an operational amplifier Q1, a resistor R connected between the inverting input terminal of the amplifier Q1 and ground, and a capacitor C connected between the output and the inverting input terminal of the amplifier Q1; a limiting inversion integrating circuit 60 having an operational amplifier Q2, a resistor R connected between the output of the operational amplifier Q1 and the inverting input terminal of the amplifier Q2, a capacitor C connected between the output and the inverting input terminal of the amplifier Q2, and voltage limiting zener diodes ZD1 and ZD2 connected in reverse series with one another and also connected in parallel with the capacitor C. The integrating circuit 58 is connected in cascade with the inversion integrating circuit 60 in a feedback loop described in the following differential equations: EQU RC(d/dt)e.sub.x =e.sub.y, and (1) EQU RC(d/dt)e.sub.y =e.sub.x, (2)
where the time constants R1, C1 are intentionally made larger than RC to thereby render the circuit slightly unstable. The voltage limiting zener diodes ZD1 and ZD2 serve to eliminate the deformation of the waveform of e.sub.y and to stabilize the amplitude thereof. The two outputs e.sub.x and e.sub.y have different phases of 90.degree. as will be expressed by the following equations: EQU e.sub.x =E sin (t/RC), and (3) EQU e.sub.y =E cos (t/RC), (4)
where E represents the voltage at the zener diodes ZD1 and ZD2. External terminals 01 and 01', 02 and 02' are connected at both ends of the resistors R and R for setting the frequency in the integrating circuits 58 and 60, and external resistors R2 and R3 are respectively connected between such terminals. The output terminals 0 and 0' of the oscillator 42 are connected to the control circuit 44 as shown in FIG. 3.
FIG. 5 shows an example of the control circuit 44. Pulse signals +ZP and -ZP outputted from the Z scale 38 in response to the variations in the Z-axis movement of the electrode 10 are inputted to the control circuit 44. In this case, as the electrode 10 advances while machining the workpiece 12, the +ZP is outputted from the Z scale 38, and as the electrode 10 retracts the -ZP is outputted.
The pulse train thus outputted from the Z scale 38 are applied to the pulse multipliers 62 and 64, respectively. Such pulse multipliers are generally known as binary rate multipliers (BRMs), and TTL IC SN7497N circuits manufactured by Texas Instruments, Inc. may be utilized.
The pulse trains thus outputted from the Z scale 38 are demultiplied through the pulse multipliers 62 and 64 to a desired factor I/N preset by input switch groups 66.sub.l through 66.sub.n such that the setting of the machining radius R of the workpiece is varied by one unit for every N pulses due to the variation in the Z-axis movement of the electrode 10.
The outputs from the multipliers 62 and 64 are in turn applied to the negative and positive input terminals of a machining radius (R) setting reversible counters 68 set at the radius R.sub.0 at the time of starting the machining operation. This initial value is executed by setting switch groups 70.sub.l through 70.sub.n, and is set into the reversible counter 68 at the time of starting the machining operation by a set switch 72.
The outputs from the reversible counter 68 are applied to multiplication type digital-to-analog converters (DACs) 74.sub.x and 74.sub.y, together with the outputs e.sub.x and e.sub.y from the two-phase oscillator 42. The outputs E.sub.x and E.sub.y from the converters 74.sub.x and 74.sub.y can be expressed as follows: EQU E.sub.x =RV sin .theta., (5) EQU E.sub.y =RV cos .theta., and (6) EQU RV=1/N{.SIGMA.(-ZP)-.SIGMA.(+ZP)}, (7)
where RV represents the digital output of the reversible counter 68. The converters 74.sub.x and 74.sub.y may be model No. AD7520 manufactured by Analog Devices, Inc. (U.S.A.).
With the control circuit 44 thus constructed, the taper angle A machined into the workpiece 12 can be specified by the 1/Z setting of switch groups 66.sub.l through 66.sub.n for determining the distribution ratio of the machining radius R relative to the length of Z-axis movement of the electrode 10, and the switch groups 70.sub.l through 70.sub.n for determining the radius R.sub.0 at the time of starting the machining operation, as follows: EQU A=tan.sup.-1 (R.sub.0 /Zm), and (8) EQU Zm=R.sub.0 .multidot.N, whereby (9) EQU A=tan.sup.-1 (1/N), (10)
where assuming R=0 when the machining depth Z is Zm, N represents the setting factor of the pulse multipliers 62 and 64, and Zm represents the final depth of the machining of the workpiece.
In the conventional discharge machining apparatus, the end of the electrode always confronts the workpiece 12 as indicated in FIG. 6A in the machining operation. Accordingly, the end of the electrode is always acted on by the discharge or the electrolysis and is thus readily consumed. When the electrode is so consumed, its end shape is varied as indicated in FIGS. 6B and 6C. Therefore, the margin RL of the portion hatched in the workpiece cannot be completely machined, but remains as indicated by the portion designated by broken lines RL' in FIG. 6C. Consequently, the configuration of the machined workpiece differs from the desired configuration, and the accuracy of the workpiece is degraded.
These problems are caused by the portion at which the electric discharge or electrolysis occurs being concentrated at the end of the electrode 10, and by the end of the electrode 10 being more consumed as compared with the other portion.